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Direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), is observed in the solar wind by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom's law for MHD turbulence, a linear relation is indeed observed for the scaling of mixed third-order structure(More)
It is shown that the inverse Lagrangian map for the solution of the Burg-ers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil's staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask(More)
We present an efficient and parsimonious algorithm to solve mixed initial/final-value problems. The algorithm optimally limits the memory storage and the computational time requirements: with respect to a simple forward integration, the cost factor is only logarithmic in the number of time-steps. As an example, we discuss the solution of the final-value(More)
The generation of large-scale magnetic field in the kinematic regime in the absence of an α-effect is investigated by following two different approaches, namely the test-field method and multiscale stability theory relying on the homogenisation technique. We show analytically that the former, applied for the evaluation of magnetic eddy diffusivities, yields(More)
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